1.1 String constraint :
When the two object are connected through a string and if the string have the following properties :
Then the parameters of the motion of the objects along the length of the string have a definite relation between them.
Ist format : - (when string is fixed)
The block B moves with velocity v. i.e. each particle of block B moves with velocity v.
If string remain attached to block B it is necessary that velocity of each particle of string is same = v (vs = v)
Now we can say that Block A also moves with velocity v.
Sol. In the above situation block B is moving with velocity v. Then speed of each point of the string is v along the string.
speed of the block A is also v
Sol. Q Block A is moving with velocity 8 ms-1.
velocity of every point on the string must be 8m/s along the string.
The real velocity of B is vB. Then the string will not break only when the compoent of vB along string is 8 m/s.
Ex.3 Find out the velocity of block B in a pulley block system as shown in figure.
Sol. In a given pulley block system the velocity of all the particle of string is let us assume v then.
10 m/s is the real velocity of block A then its component along string is v.
⇒ 10 cos 53° = v ...(1)
If vB is the real velocity of block B then it component along string is v then
vBcos37° = v ...(2)
from (1) & (2) vB cos37° = 10 cos53°
What is the velocity of block A in the figure as shown above.
Sol. The component of velocity of ring along string = velocity of A
= = vA ⇒ vA = 10 m/s
IInd format (when pulley is also moving)
To understand this format we consider the following example in which pulley is moving with velocity vp and both block have velocity vA & vB respectively as shwon in figure.
If we observe the motion of A and B with respect to pulley. Then the pulley is at rest. Then from first format.
vAP = - vBP
(-ve sign indicate the direction of each block is opposite with respect to Pulley)